Procedural Modeling. Last Time? Reading for Today. Reading for Today

Transcription

1 Last Time? Procedural Modeling Modern Graphics Hardware Cg Programming Language Gouraud Shading vs. Phong Normal Interpolation Bump, Displacement, & Environment Mapping G P R T F P D Reading for Today Reading for Today An Image Synthesizer, Perlin, SIGGRAPH 1985 & Improving Noise, Perlin, SIGGRAPH 2002 Chris Wyman, "An Approximate Image-Space Approach for Interactive Refraction, SIGGRAPH 2005

2 Today Texture Mapping Texture Mapping Common Texture Coordinate Mappings Solid Texture Procedural Textures Perlin Noise Procedural Modeling L-Systems Texture Mapping Difficulties Common Texture Coordinate Mappings Tedious to specify texture coordinates Acquiring textures is surprisingly difficult Orthogonal Cylindrical Spherical Perspective Projection Texture Chart Photographs have projective distortions Variations in reflectance and illumination Tiling problems

3 Projective Textures Projective Texture Example Use the texture like a slide projector No need to specify texture coordinates explicitly Modeling from photographs Using input photos as textures Figure from Debevec, Taylor & Malik Texture Chart Pack triangles into a single image Questions?

4 Today Texture Map vs. Solid Texture Texture Mapping Common Texture Coordinate Mappings Solid Texture Procedural Textures Perlin Noise Procedural Modeling L-Systems Solid Texturing of Complex Surfaces, Peachey, SIGGRAPH 1985 Procedural Textures Procedural Textures Advantages: easy to implement in ray tracer more compact than texture maps (especially for solid textures) infinite resolution f (x,y,z) color Disadvantages Image by Turner Whitted non-intuitive difficult to match existing texture

5 Readings for Tuesday: Perlin Noise Ken Perlin, An Image Synthesizer, SIGGRAPH 1985 & Improving Noise, SIGGRAPH 2002 Properties: Looks random, but is deterministic (always returns the same answer for a specific coordinate) Small memory footprint & fast to compute Known amplitude & frequency Smooth interpolation when zoomed in Can be combined/layered: Add multiple noise functions w/ different frequencies and amplitudes Simple arithmetic operations (thresholding, sine waves, etc.) Shade Trees, Cook, SIGGRAPH 1984 Grey: Delauney Triangulation Best triangulation of the red dots (most equilateral) A specific triangle is in the Delauney Triangle if and only if the circle defined by those 3 points does not contain any other red dot Note: Well defined when points are random. If points are on a uniform grid, we have ties... Black: Voronoi Diagram Each cell is the set of all points in the plane that claim that cell s red dot as the closest Note: The black & grey edges are perpendicular bisectors

6 Voronoi Diagram/Cells/Regions How to re-district the Netherlands into provinces so that everyone reports to the closest capital Cell edges are the perpendicular bisectors of nearby points 2D or 3D Supports efficient Nearest Neighbor queries Optimally site the next Starbucks Cellular Textures Voronoi diagram A Cellular Texture Basis Function, Worley, SIGGRAPH ml

7 Questions? Today Texture Mapping Common Texture Coordinate Mappings Solid Texture Procedural Textures Perlin Noise Procedural Modeling L-Systems Image by Justin Legakis Procedural Displacement Mapping L-Systems alphabet: {a,b} initiator: a production rules: a -> b b -> ba generations: a b ba bab babba babbabab babbababbabba babbababbabbababbabab Ken Musgrave Prusinkiewicz & Lindenmayer, The Algorithmic Beauty of Plants,

8 L-Systems Synthetic Topiary, Prusinkiewicz, James, and Mech, SIGGRAPH 1994 Animation of Plant Development Prusinkiewicz et al., SIGGRAPH 1993 Prusinkiewicz & Lindenmayer, The Algorithmic Beauty of Plants, Cellular Texturing for Architecture Feature-Based Cellular Texturing for Architectural Models, Legakis, Dorsey, & Gortler, SIGGRAPH 2001 Procedural Modeling Advantages Small representation Generate detail as needed ( infinite? resolution) Great for natural mathematical patterns and manmade engineering and design Trivial to make many duplicate objects with small variations

9 L-Systems for Cities Procedural Modeling of Buildings Procedural Modeling of Cities, Parish & Müller, SIGGRAPH 2001 Procedural Modeling of Buildings, Mueller, Wonka, Haegler, Ulmer & Van Gool, SIGGRAPH 2006 Applications Image-based Procedural Modeling of Facades Mueller, Zeng, Wonka, & Van Gool, SIGGRAPH 2007 Entertainment Gaming Education Studying botanical variation Archeological reconstruction Realism for Training Predicting the future (how will things grow over time) Urban planning (preparing for traffic) Accommodate for that growth/change Input Photograph Reconstructed 3D Geometry

10 Questions about Procedural Modeling Questions? Number of rules necessary? Cost in human designer time of creating procedural model? Re-useability of procedural model? Validation Can you build a procedural model that produces a specific target? From a photo of a specific rare wood grain, can you create a procedural model that creates texture that looks like it came from a different location of the same/similar tree? Image by Justin Legakis